Air-core photonic bandgap fiber (PBF) is an excellent choice for fiber optic gyroscope owing to its incomparable adaptability of environment. Strong and continuous polarization mode coupling is found in PBFs with an average intensity of ~-30dB, but the coupling arrives at the limit when the maximum optical path difference between the primary waves and the polarization-mode-coupling-induced secondary waves reaches ~10mm, which is corresponding to the PBF length of ~110m according to the birefringence in the PBF. Incident light with the low extinction ratio (ER) can suppress the birth of the polarization-mode-coupling-induced secondary waves, but the low-ER light obtained by the conventional Lyot depolarizers does not work here. Consequently, a large nonreciprocity and a bias error of ~13°/h are caused in the air-core photonic bandgap fiber optical gyroscope (PBFOG) with a PBF coil of ~268m.
© 2014 Optical Society of America
One of the most successful commercial fiber optical sensors, fiber optical gyroscope (FOG), has undergone a rapid development over the past 35 years, and evolved from being a promising laboratory curiosity to becoming a market product . However, FOG accuracy is generally limited by a small number of deleterious effects arising from the undesirable properties of the loop fiber, such as Shupe effects, Faraday effects, radiation effects and so on . Traditional measures, such as quadrupole symmetry winding, use of protection housing and so on, always tend to increase the complexity and cost, even decrease reliability. Fortunately, the advent of air-core photonic-bandgap fibers (PBFs) offers a radically new method to solve all of these problems, simultaneously, conveniently and reliably, due to the fact that the PBF makes the light propagate in air that has much more stable properties than SiO2 .
Currently, the PBF most suitable for the application in a FOG is based on a 7 missing cell core geometry with hexagonal air holes triangularly arranged in the cladding, as a 3 missing cell core geometry has high loss and a 19 missing cell core geometry has too many modes [4, 5]. A 7-cell PBF with no imperfections or asymmetries have little polarization dependence just like the conventional single-mode fiber (SMF). However, residual core ellipticity is inevitable in a real PBF due to unintentional deformation of the innermost ring of air holes surrounding the core during the drawing process . In our investigated PBF, as shown in Fig. 1, the core has a ratio of major to minor axis of ~1.035, and the cladding is composed of triangularly-arranged hexagonal air holes with the edge-to-edge distance d and the hole-to-hole distance Λ, herein d/Λ≈0.97. Refs [6–10] have reported that the birefringence can arise in such kind of nominally non-polarization-maintaining fiber due to the residual ellipticity of the core, and the polarization properties in a relatively short PBF (not longer than 50m) were investigated. However, hundreds of meters of fiber is always needed in a FOG, and the birefringence and polarization mode coupling of this kind of PBF in such scale of length have never been investigated, although  has reported the results on polarization maintaining hollow core PBFs up to 100m. What is more, few papers report the influence of the PBF polarization properties on the performance of a FOG, despite the fact that  has mentioned the polarization mode coupling in the PBF is an important contribution to the long-term drift in air-core FOG. It is therefore timely to have a further study on this subject. In this paper, we investigate the polarization properties arising from the residual core ellipticity in the PBFs of different lengths, as well as their influence on the nonreciprocity of a FOG.
2. Polarization mode coupling in the PBFs
When the PBF core is an ideal circle, there exist two degenerate modes with no difference in effective index. In the investigated PBF which has a residual core ellipticity, the fundamental mode would split into two orthogonally polarized modes propagating along the major and minor axis respectively, with an effective index difference on the magnitude of 10−5, as illustrated in Fig. 2,
Therefore, the guided polarization modes in the PBF are not degenerate any more owing to the birefringence. What is more, polarization mode coupling along the fiber is inevitable due to random and continuous perturbance of the birefringence. To investigate these polarization properties in the PBF, we polarize the light from an amplified spontaneous emission (ASE) source, and launch it (extinction ratio (ER) = ~30dB) into the PBF. At the other end of the PBF, an optical coherent domain polarimeter (OCDP) is employed to measure the location and intensity of the mode coupling in the PBF . Figure 3(a) shows the spectrum of the ASE source which is inside the range of operating wavelength of the PBF according to the test results of its transmission spectrum, with the mean wavelength of 1541.8nm and the corresponding coherence function given in Fig. 3(b). Note that there exists a secondary wave at the optical path difference of ~27mm, it actually comes from a defect in the OCDP other than the ASE source.
Five PBF samples of different lengths (~10m, ~33m, ~40m, ~219m and ~268m) respectively connected with a length of conventional SMF at both ends through fusion splicing are investigated in our experiments, and the test results of polarization mode coupling are presented in Fig. 4(a) and 4(b). A conventional SMF of ~300m and a PANDA fiber of ~20m are also studied for comparison as shown in Fig. 4(c) and 4(d), and the results indicate that there are no significant secondary waves in the conventional fibers except one in the PANDA fiber which results from misalignment of the incident polarized light. However, the situation is totally different in PBFs, and there are large secondary waves continuously distributed at the side of the primary wave. In Fig. 4(a), the optical path difference between the primary waves and the farthest secondary waves in the PBFs of ~10m, ~33m, ~40m is respectively d1, d2, and d3. Obviously, d3>d2>d1, and the ratio of d1, d2, d3 to the corresponding PBF length (~10m, ~33m, ~40m) is approximately ~9 × 10−5. This fact reveals that strong polarization mode coupling happens in the PBF between the two eigen axes of the birefringence induced by the residual core ellipticity, and the effective index difference is determined to ~9 × 10−5. On the other hand, it is a surprise from Fig. 4(b) that the polarization mode coupling in PBFs of ~219m and ~268m are almost the same with the maximum optical path difference d4 = ~10mm. Consequently, the polarization mode coupling seems to arrive at the limit when the maximum optical path difference reaches ~10mm, and it is corresponding to the PBF length of L0 = ~110m based on the measured birefringence, as illustrated in Fig. 5. The PBF has residual core ellipticity, and the induced birefringence, especially its eigen axes, are fluctuating along the fiber owing to external perturbance such as stress, or internal perturbance such as random fluctuation of the form and size of the core possibly arising from non stable drawing process. The random and continuous perturbance of the birefringence finally causes the special polarization behavior in the PBF which is totally different from the situation in any conventional fibers.
When we take away the polarizer following the ASE source and directly launch the light from the ASE source (ER<0.2dB) into the PBFs, as Fig. 6(a) and 6(b) demonstrates, almost no secondary waves exist in the PBFs, indicating that the low-ER light can suppress the birth of the secondary waves, which matches the analysis in  to some certain degree. Lyot depolarizer is an efficient and convenient method to reduce ER of the light, and it is generally employed in a FOG to depolarize the polarized light from integrated optic chip (IOC) . Herein we simulate the situation of a FOG, through employing a Lyot depolarizer (a length of ~2m PANDA fiber followed by a ~4m PANDA fiber with ~45° fusion splicing) to reduce the ER of the polarized ASE light to less than 0.2dB, and launching the light into the PBFs of ~40m and ~268m. Although the ER after the depolarizer is very low, the strong and continuous polarization mode coupling still exists (see Fig. 7(a) and 7(b)), which is totally different from the situation when the light from the ASE source (ER less than 0.2dB too) is directly launched into the PBFs (see Fig. 6). This interesting result is induced by the fact that the light depolarized by a Lyot depolarizer essentially differs from the ASE light. The latter is close to (not equal to of course) the natural light in the aspect of polarization , but the former is composed of a few (maybe two or four) incoherent wave-trains respectively propagating along the two axes in the PANDA fiber, and each of those incoherent wave-trains, as a local oscillation source, produces secondary waves in the PBF, moreover, the initial optical path difference caused by the high birefringence in the PANDA fibers exists among those incoherent wave-trains and it makes d3’>d3 and d4’>d4, as illustrated in Fig. 7.
3. Nonreciprocity in a FOG induced by the residual core ellipticity
Deterioration of the FOG performance in harsh environment mainly arises from fiber coil’s sensitivity to temperature, radiation, electromagnetic and so on . In the PBF, most of the mode energy (>99%) travels in air, and the fiber performance’s dependence on the environment is anticipated to be considerably reduced . We therefore replace the conventional SMF coil in a single-mode fiber optical gyroscope (SMFOG) by an equally sized PBF coil, as shown in Fig. 8, and call it PBFOG . Compared with the conventional FOG, the PBFOG has better environment adaptability and similar static performance, thus becoming an excellent choice of the next-generation FOG, but of course those issues of fiber loss, cost and so on need to be addressed at first [1–3, 14, 15].
The investigated PBF is a kind of nominally non-polarization-maintaining fiber, so naturally two Lyot depolarizers are employed between the IOC and the fiber coil to sufficiently depolarize the polarized light from the IOC (see Fig. 8) [1, 13]. The PBF coil is made up of ~268m PBF connected with two conventional SMFs, and the Lyot depolarizer is composed of a ~2m PANDA fiber followed by a ~4m PANDA fiber with ~45° alignment angle. As Fig. 9(a) demonstrates, a large number of secondary waves exist at the coupler’s port connecting PIN-FET, compared with a few big secondary waves induced by lengths of PM segments in the conventional SMFOG (see Fig. 9(b)). The test result is consistent with the aforementioned analysis, and these large mode-coupling-induced secondary waves will cause serious nonreciprocity in the PBFOG.
As illustrated in Fig. 10, it shows a simplified model of the sensing coil. While the primary wave A and an incident secondary wave B are propagating in a sensing coil, they produce a large number of secondary waves owing to polarization mode coupling, then the polarization noreciprocity arises from the interference between the zeroth, second, fourth… order secondary waves (A2i, i = 0, 1, 2, 3…) of A and the first, third, fifth… order secondary waves (B2j + 1, j = 0, 1, 2, 3…) of B . The birefringence in the PANDA fiber and the IOC is respectively ~5 × 10−4 and ~0.073, so the optical path difference (ΔL1) between the primary wave A and the secondary wave B is ≤~5.5mm when the length of the IOC and its pigtail fibers are taken account . However, the optical path difference (ΔL2) between the primary waves and the polarization-mode-coupling-induced secondary waves in the PBF coil is less than ~10mm. Consequently, it is possible that A2i and B2j + 1 can meet with each other at one point (Omeeting point) in the PBF coil due to the fact that ΔL1<ΔL2, leading to a complete interference and a bias error as a result . Our experimental result shows a bias error of ~13°/h is caused in the PBFOG, as illustrated in Fig. 11(a) which is obtained through changing the phase difference between the primary waves and the secondary waves [1, 16, 17]. The conventional SMFOG is also measured for comparison, and the bias error of this kind is negligible compared to the precision (see Fig. 11(b)). Therefore, the polarization nonreciprocity induced by the residual core ellipticity in the PBFOG is significantly larger than that in the conventional FOG, which would seriously affect the long-term stability. Some measures have to be taken, such as the optimization of the PBF’s design and drawing process to reduce the residual core ellipticity and the induced birefringence to produce a really low-birefringence non-polarization-maintaining fiber as the conventional SMF, or the intentional further increase of the ellipticity and the induced birefringence to suppress the polarization mode coupling as the conventional PMF. Conventional measures including optimization of the depolarizer length, improvement of the IOC’s ER are also helpful for suppressing the error.
To sum up, we have studied the polarization mode coupling and the birefringence induced by the residual core ellipticity in the PBFs of different lengths. The results indicate that the strong polarization mode coupling frequently happens in the PBFs with the average intensity of ~-30dB, and the birefringence caused by the residual core ellipticity makes the polarization-mode-coupling-induced secondary waves continuously distributed at the side of the primary waves. However, it is a surprise that the coupling seems to arrive at the limit when the maximum optical path difference between the primary waves and the secondary waves reaches ~10mm, which is corresponding to the PBF length of ~110m according to the birefringence. The small ER of the incident light is helpful for suppressing the birth of the secondary waves. However, the low-ER light obtained by the conventional Lyot depolarizers usually used in the PBFOG does not work here. As a result, a large nonreciprocity and a bias error of ~13°/h is caused in the PBFOG. Therefore, the issue of the polarization nonreciprocity induced by the residual core ellipticity in the PBF has to be addressed before the PBFOG has a practical application.
This work was supported by the National Natural Science Foundation of China (NSFC) under grant No. 61205077.
References and links
1. H. C. Lefèvre, The Fiber-Optic Gyroscope (Artech House, 1993).
2. H. K. Kim, M. J. F. Digonnet, and G. S. Kino, “Air-core photonic-bandgap fiber-optic gyroscope,” J. Lightwave Technol. 24(8), 3169–3174 (2006). [CrossRef]
3. M. Digonnet, S. Blin, H. K. Kim, V. Dangui, and G. Kino, “Sensitivity and stability of an air-core fibre-optic gyroscope,” Meas. Sci. Technol. 18(10), 3089–3097 (2007). [CrossRef]
4. F. Poletti, M. N. Petrovich, A. Van Brakel, and D. J. Richardson, “Hollow core photonic bandgap fibre for truly single mode operation,” in Proceedings of IEEE/LEOS Winter Topical Meeting Series (Institute of Electrical and Electronics Engineers, Sorrento, 2008), pp. 182–183.
5. M. N. Petrovich, F. Poletti, and D. J. Richardson, “Control of modal properties and modal effects in air guiding photonic bandgap fibres,” in Proceedings of ICTON 11th International Conference on Transparent Optical Networks (Institute of Electrical and Electronics Engineers, Azores, 2009), pp. 1–4. [CrossRef]
6. G. Bouwmans, F. Luan, J. C. Knight, P. StJ. Russell, L. Farr, B. Mangan, and H. Sabert, “Properties of a hollow-core photonic bandgap fiber at 850 nm wavelength,” Opt. Express 11(14), 1613–1620 (2003). [CrossRef] [PubMed]
7. M. Wegmuller, M. Legré, N. Gisin, T. P. Hansen, C. Jakobsen, and J. Broeng, “Experimental investigation of the polarization properties of a hollow core photonic bandgap fiber for 1550 nm,” Opt. Express 13(5), 1457–1467 (2005). [CrossRef] [PubMed]
8. G. Statkiewicz, T. Martynkien, and W. Urbanczyk, “Experimental characterization of the photonic bandgap holey fiber with residual core ellipticity,” in Proceedings of ICTON 7th International Conference on Transparent Optical Networks (Institute of Electrical and Electronics Engineers, Barcelona 2005), pp. 303–306. [CrossRef]
9. J. Broeng, S. E. Barkou, and A. Bjarklev, “Polarization properties of photonic bandgap fibers,” in Proceedings of Optical Fiber Communication Conference (Institute of Electrical and Electronics Engineers, Baltimore, 2000), pp. 101–103.
10. M. Wegmuller, M. Legré, N. Gisin, K. P. Hansen, T. P. Hansen, and C. Jakobwen, “Detailed polarization properties comparison for three completely different species of highly birefringent fibers,” in Proceedings of Optical Fiber Measurements (Institute of Electrical and Electronics Engineers, Boulder, 2004), pp. 119–122.
11. J. K. Lyngsø, C. Jakobsen, H. R. Simonsen, and J. Broeng, “Truly single-mode polarization maintaining hollow core PCF,” Proc. SPIE 8421, 84210C (2012). [CrossRef]
12. P. Martin, G. Le Boudec, and H. C. Lefèvre, “Test apparatus of distributed polarization coupling in fiber gyro coils using white light interferometry,” Proc. SPIE 1585, 173–179 (1992). [CrossRef]
13. B. Szafraniec and G. A. Sanders, “Theory of polarization evolution in interferometric fiber-optic depolarized gyros,” J. Lightwave Technol. 17(4), 579–590 (1999). [CrossRef]
14. S. Blin, H. K. Kim, M. J. F. Digonnet, and G. S. Kino, “Reduced thermal sensitivity of a fiber-optic gyroscope using an air-core photonic-bandgap fiber,” J. Lightwave Technol. 25(3), 861–865 (2007). [CrossRef]
15. H. K. Kim, V. Dangui, M. Digonnet, and G. Kino, “Fiber-optic gyroscope using an air-core photonic-bandgap fiber,” Proc. SPIE 5855(1), 198–201 (2005). [CrossRef]
17. B. Szafraniec, J. Feth, R. Bergh, and J. Blake, “Performance Improvements in Depolarized Fiber Gyros,” Proc. SPIE 2510, 37–48 (1995). [CrossRef]